A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations
In this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"&g...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/3/432 |
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| author | Hari M. Srivastava Javed Iqbal Muhammad Arif Alamgir Khan Yusif S. Gasimov Ronnason Chinram |
| author_facet | Hari M. Srivastava Javed Iqbal Muhammad Arif Alamgir Khan Yusif S. Gasimov Ronnason Chinram |
| author_sort | Hari M. Srivastava |
| collection | DOAJ |
| description | In this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>). The proposed method solves nonlinear boundary-value problems and integral equations in few iterations with good accuracy. Numerical comparison shows that the new method is remarkably effective for solving systems of nonlinear equations. |
| first_indexed | 2024-03-09T05:07:19Z |
| format | Article |
| id | doaj.art-bf616067aa7a40fa8188037b16f07cf4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:07:19Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-bf616067aa7a40fa8188037b16f07cf42023-12-03T12:53:49ZengMDPI AGSymmetry2073-89942021-03-0113343210.3390/sym13030432A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear EquationsHari M. Srivastava0Javed Iqbal1Muhammad Arif2Alamgir Khan3Yusif S. Gasimov4Ronnason Chinram5Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, PakistanDepartment of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, AzerbaijanDivision of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, ThailandIn this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>). The proposed method solves nonlinear boundary-value problems and integral equations in few iterations with good accuracy. Numerical comparison shows that the new method is remarkably effective for solving systems of nonlinear equations.https://www.mdpi.com/2073-8994/13/3/432nonlinear equationsgauss quadrature formulaordinary differential equation (ODE)error equationssixth-order convergencenumerical examples |
| spellingShingle | Hari M. Srivastava Javed Iqbal Muhammad Arif Alamgir Khan Yusif S. Gasimov Ronnason Chinram A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations Symmetry nonlinear equations gauss quadrature formula ordinary differential equation (ODE) error equations sixth-order convergence numerical examples |
| title | A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations |
| title_full | A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations |
| title_fullStr | A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations |
| title_full_unstemmed | A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations |
| title_short | A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations |
| title_sort | new application of gauss quadrature method for solving systems of nonlinear equations |
| topic | nonlinear equations gauss quadrature formula ordinary differential equation (ODE) error equations sixth-order convergence numerical examples |
| url | https://www.mdpi.com/2073-8994/13/3/432 |
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